Chapter 1.7, Problem 17E

a.

To determine

To graph:

Linear model for data using regression feature and find how closely models fits to data.

Explanation of Solution

Give information:

  

Graph:

  

Interpretation:

From the graph, data is written in tabulated form as below:

$x$	$-3$	$-1$	$0$	$2$	$4$
$y$	$0$	$1$	$2$	$4$	$3$

Using regression feature of the graphing utility linear model for the above tabulated data is as above,

So, best fit linear model is $y=0.46x+1.6$

b.

To determine

To calculate:

Linear model for data numerically and find how closely models fits to data.

Answer to Problem 17E

Best fit linear model is $y=0.46x+1.6$

Explanation of Solution

Give information:

  

Calculation:

Regression line is $y=0.46x+1.6$

  $\begin{array}{l}x=-3\Rightarrow y=0.46\left(-3\right)+1.6\\ =0.22\\ x=-1\Rightarrow y=0.46\left(-1\right)+1.6\\ =1.14\\ x=0\Rightarrow y=0.46\left(0\right)+1.6\\ =1.6\\ x=2\Rightarrow y=0.46\left(2\right)+1.6\\ =2.52\\ x=4\Rightarrow y=0.46\left(2\right)+1.6\\ =3.44\end{array}$

Above values can be tabulated as below:

$x$	$-3$	$-1$	$0$	$2$	$4$
Given data	$0$	$1$	$2$	$4$	$3$
Linear equation	$0.22$	$1.14$	$1.6$	$2.52$	$3.44$

This model fits the data well.